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Singular Value Decomposition

The singular value decomposition (SVD) of an m-by-n matrix A is given by   
where U and V are orthogonal (unitary) and tex2html_wrap_inline12820 is an m-by-n diagonal matrix with real diagonal elements, tex2html_wrap_inline12826, such that
The tex2html_wrap_inline12826 are the singular values of A and the first min(m,n) columns of U and V are the left and right singular vectors of A.   

The singular values and singular vectors satisfy
where tex2html_wrap_inline12840 and tex2html_wrap_inline12842 are the ith columns of U and V, respectively.

A single driver  routine, PxGESVD  , computes the ``economy size'' or ``thin'' singular value decomposition of a general nonsymmetric matrix (see table 3.4). Thus, if A is m-by-n with m>n, then only the first n columns of U are computed and tex2html_wrap_inline12820 is an n-by-n matrix. For a detailed discussion of the ``thin'' singular value decomposition, refer to [71, p. 72,].

Currently, only PSGESVD and PDGESVD are provided.

Table 3.4: Driver routines for standard eigenvalue and singular value problems

Susan Blackford
Tue May 13 09:21:01 EDT 1997